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Andrei Korobeinikov1,2,3,4, Aleksei Archibasov1,2,3,4, Vladimir Sobolev1,2,3,4

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This study simplifies complex evolutionary biology models by separating fast and slow time scales. A reduced model for RNA virus evolution accurately reflects original model results, aiding analysis.

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Area of Science:

  • Evolutionary biology
  • Computational modeling
  • Mathematical biology

Background:

  • Evolutionary models often integrate processes across vastly different timescales, complicating analysis.
  • RNA virus evolution involves both rapid selection and slower evolutionary changes.
  • Analytical study of multi-timescale models is challenging.

Purpose of the Study:

  • To develop a method for reducing the complexity of evolutionary models.
  • To simplify a mathematical model of RNA virus evolution.
  • To investigate the effectiveness of time scale separation for model order reduction.

Main Methods:

  • Applied time separation techniques to a multi-timescale evolutionary model.
  • Reduced a system of three integro-partial derivative equations to a single equation.
  • Utilized computational methods to validate the reduced model.

Main Results:

  • Successfully reduced a complex RNA virus evolution model to a single equation.
  • Demonstrated that the reduced model provides a good fit to the original model's results.
  • Confirmed the feasibility of model order reduction via time separation.

Conclusions:

  • Time scale separation is an effective strategy for simplifying complex evolutionary models.
  • The reduced model offers a computationally tractable approach to studying RNA virus evolution.
  • This method facilitates the analytical study of systems with disparate evolutionary rates.